Synchronization between transmitter and receiver is essential for correct signal acquisition. Typically, synchronization is achieved by transmitting a sequence known both at the transmitter and the receiver, receiving the transmitted sequence at the receiver, and matching the received sequence to a locally-generated replica thereof to determine the start of the sequence.
The process of matching the received sequence to the locally-generated replica includes determining time and frequency offsets between the received sequence and the replica. Typically, this is done by cross-correlating both in time and frequency the received sequence and the replica, sampling the resulting cross-correlation results to generate a cross ambiguity function (CAF) surface, and detecting a peak value in the CAF surface corresponding to estimates of the time and frequency offsets.
In practice, however, because only discrete samples of the CAF surface are calculated, determining the actual time and frequency offsets between the received sequence and the replica may not be possible. Typically, the actual time and frequency offsets are not aligned with sample points of the CAF, thereby resulting in what is known as off-bin loss and a degradation in peak detection performance.
In trying to minimize off-bin loss, conventional methods oversample the received sequence to generate a large number of CAF samples, thereby reducing off-bin loss and increasing the probability of peak detection. These methods use a temporal sampling rate that is high enough to place at least three sample points on the main peak of the autocorrelation function of the sequence. For certain types of signals, such as binary phase-shift keyed signals with rectangular symbols (BPSK-R), this corresponds to a sampling rate that is twice the chip rate (2 samples/chip) of the received sequence.
It has been shown, however, that the complexity of initial synchronization processing increases with more than the square of the temporal sampling rate, and that the storage required increases linearly with the sampling rates in time and frequency. Using oversampling to limit off-bin loss, accordingly, significantly affects the cost and complexity of the receiver.
What is needed, therefore, are methods and systems for initial synchronization processing that provide reduced cost and complexity at the receiver while maintaining a good peak detection performance.